Is there anyway to make particles have an influence area around them that will let them collide, without having to turn them into rigid bodies?
You can add a force to the particles to effectively repel each other as in this answer https://blender.stackexchange.com/a/84426/29586. It isn’t ideal as it relies on the particles being all the same size and it isn’t physically accurate (but is a quick and dirty method). 

Another option is to use the Molecular Script add-on (http://pyroevil.com/molecular-script-docs/) which physically simulates the particle collisions.